Relaxed trajectories of nonconvex nonlinear Hilfer fractional impulsive control system

A non-convex control system governed by a nonlinear impulsive evolution equation of Hilfer fractional order in a Banach space is considered. Existence of admissible state-control pair is established. Then the introduction of suitable measure-valued control, convexifies the system and the relaxed system is obtained. Further, relaxation theorem for the described class are proved along with the existence of optimal relaxed control.